ON PADDLE WHEELS. 



133 



Having first found the value of S, and assumed a value of y not very far from the truth, 

 we can prove it with very little trouble by the above formula. If we find too great a value 

 for S", we take off a little from our assumed value of y, and if the second result differ still 

 from the true value of S", we make a proportion of the differences ; the third result will be 

 as near as can be desired, if the differences are small. In this manner the following tables 

 were calculated, in which the extreme radius of the wheel has been assumed equal to 10, or, 

 which is the same thing, one-tenth of the radius has been taken as unity. The immersion 

 is given in the upper line, and the radius of the rolling circle in the first column on the left : 

 the decimal fraction corresponding to the given immersion and radius of the rolling circle, 

 expresses the portion of the depth of the float included between its upper edge and its centre 

 of pressure. Thus, if the immersion be 4, and the radius of the rolling circle 7'4 (see 

 Table I.), the centre of pressure will be situated at a distance of 0'557 of the depth of the 

 float from its upper edge. 



TABLE I. Extreme radius = 10 ; Depth of float = 2. 



